Using suitable identity, find the value of 87^3+ 13^3/
87^2 −87 ×13 + 13^2

An example of the ratio 13:4 is this: A group of 13 students got 4 boxes of pizza.

A ratio refers to an expression that indicates the number of times a value contains another. For instance, in the expression above, we can see that there is an expression that shows that 13 students are meant to share 4 boxes of pizza. A ratio tells us how many of one quantity are found in another one.

The proportions being compared in a ratio are never meant to be equal to zero. So, an example of the ratio above is a group of 13 students who got 4 boxes of pizza.

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Answer:

Step-by-step explanation:

If he rides 21 miles in 3 hours, you gotta find the unit rate

21 divided by 3 equals 7

so 7 miles for 1 hour

7 times 4 = 28

he will ride 28 miles in 4 hours!

Hope this helps

1. We can calculate the slope (m): m = 498.7

2. We have the equation of the trend line: y = 498.7x - 1009.75

3.  The forecasted sales for year 5 is approximately 1483.75.

4.  The forecasted sales for year 6 is approximately 1982.45.

To use the Linear Trend Equation for forecasting sales in year 5 and 6, we need to calculate the equation of the trend line first. The formula for a linear trend line is:

y = mx + b

Where:

y = dependent variable (sales)

x = independent variable (year)

m = slope of the line

b = y-intercept

To find the slope (m) and y-intercept (b), we can use the least squares method or the method of linear regression. However, since we only have four data points, we'll use a simplified version of the linear regression formula:

m = [(nΣxy) - (ΣxΣy)] / [(nΣx^2) - (Σx)^2]

b = (Σy - mΣx) / n

Let's calculate the values:

n = number of data points = 4

Σx = sum of years = 1 + 2 + 3 + 4 = 10

Σy = sum of sales = 230 + 235 + 239 + 243 = 947

Σxy = sum of (year * sales) = (1 * 230) + (2 * 235) + (3 * 239) + (4 * 243) = 4861

Σx^2 = sum of (year^2) = (1^2) + (2^2) + (3^2) + (4^2) = 30

Now we can calculate the slope (m):

m = [(nΣxy) - (ΣxΣy)] / [(nΣx^2) - (Σx)^2]

= [(4 * 4861) - (10 * 947)] / [(4 * 30) - (10^2)]

= [19444 - 9470] / [120 - 100]

= 9974 / 20

= 498.7

Next, let's calculate the y-intercept (b):

b = (Σy - mΣx) / n

= (947 - (498.7 * 10)) / 4

= (947 - 4987) / 4

= -4039 / 4

= -1009.75

Now we have the equation of the trend line:

y = 498.7x - 1009.75

To forecast sales in year 5, substitute x = 5 into the equation:

y = 498.7 * 5 - 1009.75

= 2493.5 - 1009.75

= 1483.75

Therefore, the forecasted sales for year 5 is approximately 1483.75.

To forecast sales in year 6, substitute x = 6 into the equation:

y = 498.7 * 6 - 1009.75

= 2992.2 - 1009.75

= 1982.45

Therefore, the forecasted sales for year 6 is approximately 1982.45.

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The Function is decreasing over the interval π/2 < x < 3π/2.The amplitude of the function is 15, the period of the function is 2π, the midline of the function is y = 18, the function is increasing over the interval 0 < x < π, and the function is decreasing over the interval π/2 < x < 3π/2.

The given equation y = 15sin(x) + 18 models the height of a rider with respect to the rotation of the ride and is represented as a graph in the xy-coordinate plane. We are to find out the amplitude, period, midline of the function and the intervals over which it is increasing or decreasing.

Amplitude:The amplitude of the function is the coefficient of the trigonometric function and here, it is 15. Therefore, the amplitude of the function is 15.Period:The period of the function is given by the formula 2π/b. Here, b is the coefficient of x. Therefore, the period of the function is 2π/1 which is 2π.

Midline:The midline of the function is the average of the maximum and minimum heights. The maximum height is 33 m and the minimum height is (33 - 2 × 15) = 3 m. Therefore, the midline of the function is y = (33 + 3)/2 which is y = 18.

The function is increasing over the interval 0 < x < π:To determine the interval over which the function is increasing, we need to find the interval over which sin(x) is increasing.

Since sin(x) is an increasing function over the interval 0 < x < π/2, the entire function 15sin(x) is also increasing over that interval. Therefore, the function is increasing over the interval 0 < x < π.

The function is decreasing over the interval π/2 < x < 3π/2:To determine the interval over which the function is decreasing, we need to find the interval over which sin(x) is decreasing. Since sin(x) is a decreasing function over the interval π/2 < x < π, the entire function 15sin(x) is also decreasing over that interval.

Therefore, the function is decreasing over the interval π/2 < x < 3π/2.The amplitude of the function is 15, the period of the function is 2π, the midline of the function is y = 18, the function is increasing over the interval 0 < x < π, and the function is decreasing over the interval π/2 < x < 3π/2.

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Complete Question:

On a number​ line, the coordinates of​ X, Y,​ Z, and W are −8​, −5​, 4​, and 6​, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. [tex] \overline{XY} [/tex] and [tex] \overline{ZW} [/tex]

Answer:

[tex] \overline{XY} = 3 [/tex]

[tex] \overline{ZW} = 2 [/tex]

They are not congruent

Step-by-step explanation:

Length of segment XY:

Coordinate of X = -8

Coordinate of Y = -5

[tex] \overline{XY} [/tex] = |-8 -(-5)| = |-8 + 5| = 3

Length of ZW:

Coordinate of Z = 4

Coordinate of W = 6

[tex] \overline{ZW} [/tex] = |4 - 6| = 2

[tex] \overline{XY} [/tex] ≠ [tex] \overline{ZW} [/tex], therefore, they are not congruent.

Answer:

=499,750,000,000

Step-by-step explanation:

2 × 10-12 =500000000000  

4 × 10-9=250000000

500000000000-250000000=499,750,000,000

I hope this helps (:

Answer:

so if it takes 3/1_2 cups of flour to make 3 dozen cookies then it must take 1/2 cups of flour to make 36 cookies because 12x3 equals 36

Step-by-step explanation:

Answer:

1.3

Step-by-step explanation:

Answer:

To find an expression that is equivalent to `y = x^2 + 8x + 18`, we can try to complete the square, factorize, or use the quadratic formula.

Completing the square:

We can add and subtract (8/2)^2 = 16 to the right-hand side of the equation to get:

y = x^2 + 8x + 18 + 16 - 16

y = (x + 4)^2 + 2

So an equivalent expression for `y = x^2 + 8x + 18` is `y = (x + 4)^2 + 2`.

Factorizing:

We can try to factorize the quadratic expression on the right-hand side of the equation. To do this, we need to find two numbers whose sum is 8 and whose product is 18. These numbers are 2 and 6, so we can write:

y = x^2 + 2x + 6x + 18

y = (x^2 + 2x) + (6x + 18)

y = x(x + 2) + 6(x + 3)

y = (x + 2)(x + 6)

So an equivalent expression for `y = x^2 + 8x + 18` is `y = (x + 2)(x + 6)`.

Using the quadratic formula:

We can use the quadratic formula to solve for x in the equation `y = x^2 + 8x + 18`. The quadratic formula states that for an equation of the form `ax^2 + bx + c = 0`, the solutions for x are given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In our case, a = 1, b = 8, and c = 18. Substituting these values into the quadratic formula, we get:

x = (-8 ± sqrt(8^2 - 4(1)(18))) / 2(1)

x = (-8 ± sqrt(4)) / 2

x = -4 ± 1

So the solutions for x are x = -5 and x = -3. If we substitute these values into the original equation `y = x^2 + 8x + 18`, we get:

When x = -5, y = (-5)^2 + 8(-5) + 18 = 5 - 40 + 18 = -17

When x = -3, y = (-3)^2 + 8(-3) + 18 = 9 - 24 + 18 = 3

So an equivalent expression for `y = x^2 + 8x + 18` is `y = (x + 5)(x - 3)`.

Answer:

8 & 12

Step-by-step explanation:

x+y=20 [The sum of two numbers is twenty]

3x=2y [Three times the smaller is equal to twice the larger]

.

x=20-y [Solve for x]

3(20-y)=2y [Substitute (x=20-y) into the second equation]

60-3y=2y [Solve for y]

60=5y

60/5=y

12=y

.

x+y=20 [Plug (y=12) back into either of the original equations]

x+12=20 [solve for x]

x=8

.

Answer:

The smaller number is 8

The larger number is 12

Step-by-step explanation:

Let the smaller number be x

Let the larger number be y

Translate the question and solve ;

[tex]x +y = 20\\3(x) =2(y) \\\\\begin{bmatrix}x+y=20\\ 3x=2y\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:x+y=20:\quad x=20-y\\\\\mathrm{Subsititute\:}x=20-y\\\\\begin{bmatrix}3\left(20-y\right)=2y\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:3\left(20-y\right)=2y:\quad y=12\\\\\mathrm{For\:}x=20-y\\\\\mathrm{Subsititute\:}y=12\\\\x=20-12\\\\Simplify\\\\x =8\\\\x=8,\:y=12[/tex]

Answer:

tell a teacher at school or call child sevices.

Answer:

lollllllllllll ty for points

The range of c for which the optimal solution does not change is c = 2.

To determine the range of c for which the optimal solution does not change, we need to identify the values of c for which the objective function remains parallel to the original objective function 2x1 + 5x2.

In the original problem, the objective function is Z = 2x1 + 5x2.

If we change the coefficient of x1 to c, the new objective function becomes Z = cx1 + 5x2.

To keep the optimal solution unchanged, we need the direction of the objective function to remain the same. This means that the slope of the new objective function should be the same as the original objective function (2x1 + 5x2).

The slope of the new objective function is equal to the coefficient of x1, which is c. Therefore, for the optimal solution to remain the same, the value of c must be equal to 2.

So, the range of c for which the optimal solution does not change is c = 2.

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30

Look at the next part in the order it goes up, straight up again then down then up, which probably means that you are gonna go up again instead of going down

all in the up's and down's lol

Answer:

n = 75

Step-by-step explanation:

Step 1: Write equation

-n = -75

Step 2: Divide both sides by -1

n = 75

Step 3: Check

Plug in n to verify it's a solution.

-75 = -75

Answer:

No solutions or ∅

Step-by-step explanation:

Do the algebra:

[tex]-\frac{1}{3}+\frac{2}{3}m=\frac2 3 m - \frac 2 3 \\\\\frac 2 3 m = \frac 2 3 m - \frac 2 3\\\\0=-\frac 2 3[/tex]

Since 0 ≠ -2/3, this equation has no solutions.

Hope this helped :)

Answer:

well i'm in 8h grade and haven't learned this yet

Step-by-step explanation:

sorry.

BTW like your todoroki picture^^

Answer:

it is irrational number

Answer:

  adjust the weights until balance is achieved

Step-by-step explanation:

Start with all of the beam weights in their 0 position.

Move the heaviest weight to successive positions farther from 0 until the beam falls. Move it back one.

Move the next-heaviest weight to successive positions farther from 0 until the beam falls. Move it back one.

Move the lightest weight along the scale away from 0 until the beam is centered in the space.

The weight of the object in the tray is the sum of the marks on the scales associated with the three weights.

_____

It helps if the device is "calibrated" before you add anything to the pan. When the pan is empty and all beam weights are in their 0 position, the beam should be centered in its space. If not, adjust the zeroing device until it is.

The attached picture shows a typical laboratory triple-beam balance. It is capable of measuring weights up to 610 grams with a resolution of 0.1 grams or better.

To find the composite functions (fog)(x) and (gof)(x) using the given functions f(x) = 2x - 4 and g(x) = 2, we substitute one function into the other based on the order indicated. (fog)(x) = 0, (gof)(x) = 2, (fog)(7) = 0, and (gof)(7) = 2.

The value of (fog)(7) and (gof)(7) can be determined by evaluating the composite functions at x = 7.

a. To find (fog)(x), we substitute g(x) into f(x): (fog)(x) = f(g(x)) = f(2). Since g(x) = 2, we replace g(x) with 2 in f(x): f(2) = 2(2) - 4 = 4 - 4 = 0. Therefore, (fog)(x) = 0.

b. To find (gof)(x), we substitute f(x) into g(x): (gof)(x) = g(f(x)) = g(2x - 4). Since f(x) = 2x - 4, we replace f(x) with 2x - 4 in g(x): g(2x - 4) = 2. Therefore, (gof)(x) = 2.

c. To find (fog)(7), we evaluate (fog)(x) at x = 7: (fog)(7) = 0.

d. To find (gof)(7), we evaluate (gof)(x) at x = 7: (gof)(7) = 2.

Therefore, (fog)(x) = 0, (gof)(x) = 2, (fog)(7) = 0, and (gof)(7) = 2.

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1. W = {(a, 0, b) | a, b ≤ R} is a subspace of R³.

2. W = {(a, 2, b) | a, b ≤ R} is not a subspace of R³.

3. W  = {au + Bula | ß E R} is a subspace of V.

4. In a vector space V, Ov = 0 for all v € V.

1. To show that W = {(a, 0, b) | a, b ≤ R} is a subspace of R³, we need to demonstrate that it satisfies three conditions:

(i) it contains the zero vector,

(ii) it is closed under vector addition, and

(iii) it is closed under scalar multiplication.

The zero vector is (0, 0, 0), which is in W. For closure under vector addition, let (a₁, 0, b₁) and (a₂, 0, b₂) be arbitrary vectors in W. Their sum is (a₁ + a₂, 0, b₁ + b₂), which is also in W. Similarly, for closure under scalar multiplication, if (a, 0, b) is in W, then k(a, 0, b) = (ka, 0, kb) is also in W. Therefore, W is a subspace of R³.

2. To determine whether W = {(a, 2, b) | a, b ≤ R} is a subspace of R³, we need to check the three conditions mentioned above. The zero vector (0, 0, 0) is not in W since it does not satisfy the condition a, b ≤ R. Therefore, W does not contain the zero vector and fails to meet the requirements of a subspace. Hence, W is not a subspace of R³.

3. To prove that W = {au + Bula | ß E R} is a subspace of V, we need to show that it satisfies the conditions of a subspace. The zero vector is in W since for ß = 0, we have 0u + 0ula = 0. For closure under addition, let x = au + Bula and y = cu + Dula be arbitrary vectors in W. Their sum is x + y = (a + c)u + (B + D)ula, which is also in W. Similarly, for closure under scalar multiplication, if x = au + Bula is in W, then kx = (ka)u + (kB)ula is also in W. Therefore, W is a subspace of V.

4. In a vector space V, the zero vector Ov is defined as the unique vector that satisfies the equation v + Ov = v for any v in V. By the properties of vector addition, we have v + Ov = Ov + v = v. Therefore, Ov = 0 for all v € V, where 0 is the zero vector in the vector space V.

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Answer:

You have $23 left to spend on diapers for Jake.

Step-by-step explanation:

To be able to find the answer, first you need to calculate the amount you would spend on blanket:

$115*15%=$17.25

Now, you need to calculate the amount you would spend on toys:

$115*25%=$28.75

Then, you need to calculate the amount you would spend on clothes:

$115*40%=$46

Now, you need to add this values up and subtract the total from $115:

$17.25+$28.75+$46=$92

$115-$92=$23

According to this, the answer is that you have $23 left to spend on diapers for Jake.

Answer:

You have $23 left to spend on diapers for Jake. To find the answer, first you need to figure out the amount you would spend on blanket.  $115x15%=$17.25 . Next, you need to find the amount of money you spent on toys.  $115x25%=$28.75 , then, you'll find the amount of money you spend on clothes.  $115x40%=$46 . Now, add the values up and subtract the total from $115. this gives you $23 . This means the answer is $23 are left to spen on diapers for Jake.

Step-by-step explanation:

Answer:

Which shapes cover more of the plane" means that we are comparing the areas covered by the different types of shapes. In these patterns, two triangles match up to one rhombus, and three triangles match up to one trapezoid.

In both Pattern A and Pattern B, the first hexagonal part is made up of 7 triangles, 4 rhombuses, and 3 trapezoids.

The first hexagonal part is repeated across the pattern, so whichever type of shape covers the most area of this first part also covers the most area in the whole pattern.

hope it helps

Answer:

They still need to make 1/2 the amount of cupcakes.

Step-by-step explanation:

First, we need to find out how much is 1/4 of 120 to see how many cupcakes she made.

To do this, we just need to multiply.

[tex]\frac{1}{4} *120=30[/tex]

So, she made 30 cupcakes.

And the given information was that he already made 30 cupcakes as well. So, add the amount that they have done.

30+30= 60

They've made 60 cupcakes. But we need to find out how many are left to make, so we need to subtract 60 from 120.

120-60= 60

They need to make 60 more cupcakes, which is 1/2 of 120.

Answer:They still need to make 1/2 the amount of cupcakes.

Step-by-step explanation:

First, we need to find out how much is 1/4 of 120 to see how many cupcakes she made.

To do this, we just need to multiply.

So, she made 30 cupcakes.

And the given information was that he already made 30 cupcakes as well. So, add the amount that they have done.

30+30= 60

They've made 60 cupcakes. But we need to find out how many are left to make, so we need to subtract 60 from 120.

120-60= 60

They need to make 60 more cupcakes, which is 1/2 of 120.

Step-by-step explanation:

The minimum possible product of three different numbers in the set {-8, -6, -4, 0, 3, 5, 7} is -192.

We can first arrange the numbers in increasing order in order to get the smallest possible product of the three different numbers in the given set.

{-8, -6, -4, 0, 3, 5, 7} → {-8, -6, -4, 0, 3, 5, 7}

The three lowest figures are -8, -6, and -4. These three integers added together yield:

-8 × -6 × -4 = -192

Any other three numbers in the set will have a product that is either positive or contains positive numbers, in which case it will be bigger than -192. As a result, the smallest possible product of the trio of numbers in this set is -192.

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Answer:

y= -40

Step-by-step explanation:

Answer:

y=-40

Step-by-step explanation:

subtract 5 from both sides

cancel out 5

y/-4=10

times -4 on both sides

y=-40

Answer:

300 coins

Step-by-step explanation:

Answer:

use y=mx+b formula

Step-by-step explanation:

figure out what the "y" "m" and "x" is. then y= whatever X is + whatever B is.

Answer:

[tex]7^5[/tex]

Step-by-step explanation:

When multiplying numbers with the same base (in this case the base is 7), the exponents add. So

-6+16-5=5

So the answer is [tex]7^5[/tex]